It well-known that there are twenty “proteinogenic” amino acids—those capable of creating proteins—in eukaryotes (i.e., lifeforms with nucleated cells). When biologists first began to realize that DNA synthesizes RNA, which synthesizes amino acids, it was not yet known how many DNA bases (the vocabulary being A, T, C, and G) were required to code an animo acid. It turns out the answer is three: each codon is a base triple, each corresponding to an amino acid. However, one might have deduced that answer ahead of time using some basic algebra, as did Soviet-American polymath George Gamow. Given that one needs at least 20 aminos (and admitting that some redundancy is not impossible), it should be clear that pairs of bases will not suffice to uniquely identify the different animos: 42 = 16, which is less than 20 (+ some epsilon). However, triples will more than suffice: 43 = 64. This holds assuming that the codons are interpreted consistently independently of their context (as Gamow correctly deduced) and whether or not the triplets are interpreted as overlapping or not (Gamow incorrectly guessed that they overlapped, so that a six-base sequence contains four triplet codons; in fact it contains no more than two).
All of this is a long way to link back to the idea of counting entities in phonology. It seems to me we can ask just how many features might be necessary to mark all the distinctions needed. At the same time, Matamoros & Reiss (2016), for instance, following some broader work by Gallistel & King (2009), take it as desirable that a cognitive theory involve a small number of initial entities that give rise to a combinatoric explosion that, at the etic level, is “essentially infinite”. Surely similar thinking can be applied throughout linguistics.
References
Gallistel, C. R., and King, A. P.. 2009. Memory and the Computational
Brain: Why Cognitive Science Will Transform Neuroscience. Wiley-Blackwell.
Matamoros, C. and Reiss, C. 2016. Symbol taxonomy in biophonology. In A. M. Di Sciullo (ed.), Biolinguistic Investigations on the Language Faculty, pages 41-54. John Benjmanins Publishing Company.